Calculate $\sqrt{75x} \cdot \sqrt{2x} \cdot \sqrt{14x}$ . Express your answer in simplest radical form in terms of $x$.
Answer: Writing everything in terms of prime factorizations, the given expression is $\sqrt{3 \cdot 5^2 \cdot 2 \cdot 2 \cdot 7 \cdot x^3} = \sqrt{(2^2 \cdot 5^2 \cdot x^2) \cdot (3 \cdot 7 \cdot x)} = \boxed{10x \sqrt{21x}}$.